A boat, which has a speed of 5km/h in still water, crosses a river of width 1km along the shortest path possible in 15 minutes. Find the velocity of the river?

1 Answer
Roy Ø.
Jun 7, 2018

The river is moving at a speed of 3 km/h.

Explanation:

If the speed of the river is constant over the stretch that the boat is sailing, we can use Pythagoras:
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If the river had been still, the boat would have moved from A to B, 1 km.
Instead, because the water is moving, the boat moves from A to C,
This stretch must be #5/4 km = 1.25 km#, since 15 min. = #1/4# hour, in which time the boat moves #5/4 km#.

According to Pythagoras,
#CB^2=^AC^2-AB^2#
#=(5/4)^2-1^2#
#=25/16-1=9/16#
Therefore #BC=sqrt(9/16)=3/4#

As the river, therefore, moves #3/4 km# in #1/4# hour, it follows that the speed is 3 km/h

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